Getting Started 
Misconception/Error The student is unable to correctly represent the problem with an equation. 
Examples of Student Work at this Level The student:
 Attempts to solve the problem using a computational approach but is unable to do so correctly.
 Writes an expression instead of an equation. The student provides answers such as 6 + 1100c or .
 Writes an incorrect equation such as 1110x = 6 or 10x = 1110.Â

Questions Eliciting Thinking Can you restate the problem in your own words? What is the unknown?
What other quantities are described in this problem? How are the quantities related?
Can you draw a diagram to help you visualize the problem? 
Instructional Implications Help the student understand that writing and solving equations is an effective problem solving strategy. Provide mathematical and realworld contexts that describe unknown quantities that can be represented by variables and variable expressions. Ask the student to identify the unknown and clearly define a variable to represent it. For example, guide the student to begin by defining the unknown quantity as the â€śnumber of cars in each parking lotâ€ť and assign a variable (e.g., x) to represent it. Then guide the student to consider other quantities described in the problem (e.g., the number of parking lots and the total number of cars) and to verbally describe how these quantities are related. Assist the student in writing an equation that models this relationship (e.g., 6x = 1110). Then relate the equation back to the problem description.
Discourage the student from writing an equation such as x = 1110 Ă· 6, which reflects a computational procedure for solving the problem rather than a relationship among the quantities described in the problem. Explain that although this equation is equivalent to others written, it is better to write equations that model relationships. Explain that as problem contexts become more complex (e.g., those represented by multistep linear equations, quadratic equations, and exponential equations), it will be much easier to model relationships with an equation and then solve the equation rather than attempt a computational strategy.
Provide additional opportunities to write and solve equations to solve realworld and mathematical problems. 
Moving Forward 
Misconception/Error The student solves the problem by writing a numerical expression or an equation that reflects a numerical procedure. 
Examples of Student Work at this Level The student correctly solves the problem but writes an expression such as 1110 Ă· 6 or an equation such as 1110 Ă· 6 = x.

Questions Eliciting Thinking What is an expression? Is it different from an equation? In what way?
Can you draw a diagram to help you visualize the problem?
Can you write an equation that shows the relationship among the quantities in this problem? 
Instructional Implications Model writing the equation as 6x = 1110 and explain how this models the relationship among the quantities in the problem. Explain that an equation such as x = 1110 Ă· 6 reflects a computational procedure for solving the problem rather than modeling the relationship among the quantities. Further explain that although this equation is equivalent to others written, it is better to write equations that model relationships. Explain that as problem contexts become more complex (e.g., those represented by multistep linear equations, quadratic equations, and exponential equations), it will be much easier to model relationships with an equation and then solve the equation rather than attempt a computational strategy.
Provide additional opportunities to write and solve equations to solve realworld and mathematical problems. 
Almost There 
Misconception/Error The student is unable to correctly solve the equation and/or interpret the solution. 
Examples of Student Work at this Level The student writes a correct equation that models the relationship among the variables but makes an error in solving the equation.
The student describes the solution as:
 The total number of cars.
 The number of parking lots.
 A specific number (e.g., 6660).
 A set of instructions for a calculation (e.g., â€śYou divide 1110 by 6â€ť).

Questions Eliciting Thinking I think you made a small error; can you find and fix it?
Can you be more specific in describing the solution? What quantity in the problem is equal to 185? What does the 185 represent? 
Instructional Implications Provide feedback to the student and allow the student to revise his or her work. Discuss strategies for solving onestep equations involving rational numbers.
Encourage the student to be explicit when defining a variable or describing a solution. Remind the student that a variable represents an unknown quantity, so an appropriate definition of a variable should include a numerical reference (e.g., x represents the number of cars per parking lot, not just â€ścarsâ€ť). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student writes an equation such as 6x = 1110 and correctly solves it. The student explains that:
 The number of parking lots times the number of cars per parking lot is equal to the total number of cars, and
 Each parking lot can hold 185 cars.

Questions Eliciting Thinking How did you know to divide by six to solve your equation?
How can you check your solution? 
Instructional Implications Pose the problem, â€śIf there are a total of 1110 parking spaces in seven parking lotsâ€”one small lot with 30 spaces and six larger lots that each have an equal number of spacesâ€”how many spaces are in each of the six larger lots?â€ť Ask the student to write and solve an equation that models the relationship among the quantities and variable.
Review solving equations of the form x + p = q and consider using MFAS task Center Section.
Review operations with fractions, and then consider using MFAS task Equally Driven, which assesses the studentâ€™s ability to write equations involving nonnegative rational numbers. 